Problem: Solve for $n$, $ \dfrac{6}{8n} = -\dfrac{n - 8}{2n} - \dfrac{8}{6n} $
Answer: First we need to find a common denominator for all the expressions. This means finding the least common multiple of $8n$ $2n$ and $6n$ The common denominator is $24n$ To get $24n$ in the denominator of the first term, multiply it by $\frac{3}{3}$ $ \dfrac{6}{8n} \times \dfrac{3}{3} = \dfrac{18}{24n} $ To get $24n$ in the denominator of the second term, multiply it by $\frac{12}{12}$ $ -\dfrac{n - 8}{2n} \times \dfrac{12}{12} = -\dfrac{12n - 96}{24n} $ To get $24n$ in the denominator of the third term, multiply it by $\frac{4}{4}$ $ -\dfrac{8}{6n} \times \dfrac{4}{4} = -\dfrac{32}{24n} $ This give us: $ \dfrac{18}{24n} = -\dfrac{12n - 96}{24n} - \dfrac{32}{24n} $ If we multiply both sides of the equation by $24n$ , we get: $ 18 = -12n + 96 - 32$ $ 18 = -12n + 64$ $ -46 = -12n $ $ n = \dfrac{23}{6}$